Conceptual illustration of the MLP formalism. The bold line represents the MLP, while the faint line corresponds to a proton undergoing exaggerated multiple Coulomb scattering.
Plot of the derived effective mean chord length as a function of pixel rotation angle.
Schematic of the GEANT4 simulation geometry used to model an ideal pCT system.
(a) The Herman head phantom. Reconstructed images corresponding to the cycle of minimum relative error with (b) constant chord length, (c) exact chord length, and (d) effective mean chord length.
Distribution of reconstructed relative stopping powers with constant chord length, exact chord length, and effective mean chord lengths.
Schematic of the rotated pixel geometry. The pixel vertices are denoted by points A, B, C, and D. The linear functions joining these points are labeled , , , and . A simplified straight line proton path is given as an example, illustrating the discrete stepping nature of the MLP. The step size is denoted by . The chord length for this example is shown in bold.
Derivation of the point on the axis at which the chord length through a pixel is equal to the step size of the MLP procedure. Through symmetry, the same method can be used to derive for the positive axis.
Results of a Guassian fit to histograms of reconstructed bone and brain regions in the relative stopping power images. The mean value with 95% confident limit and standard deviation are given.
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